When asked to compare the severity of sea-transportation between the North Sea1 and the South China Sea, most engineers side with the former, which they deduce from comparing sea-states. So, it’s rare to not get a blank stare from people when I say they may not be right.2 Here’s why. Let’s take a look at practiced barge motion design criteria in each.

Table 1: Barge motion criteria for medium sized barges

Parameter

North Sea

South China Sea

Length, L (m)

>76.0

91.4

Width, B (m)

>23.0

27.4

Roll angle, $\alpha$ (°)

20.0

12.5

Roll period, $T_r$ (s)

10

5

Pitch angle, $\beta$ (°)

12.5

8

Pitch period, $T_p$ (s)

10

5.5

Heave, gh

0.2g

0.2g

where, $\alpha$ and $\beta$ are roll and pitch single amplitude of angular accelerations respectively (in degrees), together with corresponding full cycle periods (in seconds); and h is heave single amplitude of linear acceleration (either in terms of g, or in meters).

At first look, with all motion parameters greater, this may still look like the North Sea is governing over the South China Sea. But is it really? To be sure, let’s convert these into accelerations and resulting inertial forces.

Maximum acceleration, in a simple harmonic motion without phase info., may be computed as follows:

where, Tr, Tp, and Th are full cycle periods associated with roll, pitch and heave respectively (s). They are given in Table 1.

Table 2: Accelerations

$\theta_r$ (rad/s2)

$\theta_p$ (rad/s2)

gh (m/s2)

North Sea

0.14

0.09

1.96

South China Sea

0.34

0.22

1.96

Increase (%)

143%

144%

–

What? How? Well, it is due to the full cycle period associated with motions, the proverbial elephant in the room, because most people read or regard full cycle periods as some sort of meta information. In the case of the South China Sea, however, nonlinearly lower full cycle periods in the denominator drive accelerations up. In turn, inertial forces increase as a consequence of higher accelerations (Newton’s second law of motion).3

$r_x$ and $r_y$ are radii of gyration along head and beam directions respectively, and

$GM_T$ and $GM_L$ are metacentric height in transverse and longitudinal directions respectively

There is a reason full (motion) periods are engineered for manned vessels, which is to make motions humanely tolerable as the graph below shows.4

Boundary of depression and intolerable ranges can occur for very low accelerations, if periods are too low. Whereas a combination of acceleration and its corresponding average frequency of oscillation determines the level of comfort aboard.

However, marine cargo transports often involve unmanned dummy barges, for which human response is not seen as a governing requirement, and are therefore OK to operate at lower periods of motion. High dynamic acceleration is often a result of small period of motion, as seen in the case of South China Sea pertaining to unmanned cargo barges.

One way to manage this is by optimising (static) metacentric height, GM, by keeping it sufficiently high from greater initial stability considerations — but not excessively high, to warrant low periods of motion. This would not only reduce dynamic accelerations, but also help improve human response, where essential.

Effect of cargo position on inertia forces (Oct 22, 17)

While working on a project recently, I took the opportunity to develop the effect of cargo position on sea-transport forces in unrestricted open-seas (in terms of W, which is the dry weight of cargo), and extend it to profile all vessel types described in 0030/ND.

For non-standard motion responses, particularly in benign environments that exhibit lower single amplitude motion and lower full cycle period, the following code could be used. It requires all values to be input.

I’ve found not Mechanical, Metocean, or Structural engineers, but only Naval architects are usually quick to recover from their stagger as they are able to quickly bring in other factors into perspective. ↩